The present invention relates to a simulation method for an object associated with a problem occurring in reality is probabilistic and, more particularly, to a change prediction method or a film profile prediction method to which the simulation method is applied.
As well known, in manufacturing a semiconductor device, the step of producing a thin film on a substrate is present. As a method of producing the thin film, a Chemical Vapor Deposition (CVD) method is frequently employed
In recent years, with improvement on the technique, the thickness of a circuit pattern on the substrate must be 1 .mu.m or less, and a thin film produced on the pattern must be also micropatterned according to the decrease in thickness. When the integration density of the device is increased, a burying characteristic (step coverage) in a pattern with a step difference (trench) can become a problem.
For example, by using a reduced-pressure CVD method, and by using silane (SiH.sub.4) and argon (Ar) gas as a source gas and a carrier gas, a polycrystalline silicon film is formed on the inner surface of a trench formed in a wafer and having an aspect ratio of about 10 under the conditions: a wafer temperature of 700.degree. C., a pressure of 25 Torr; an Ar flow rate of 4.5 l/min; and an SiH.sub.4 flow rate of 1.0 l/min. The film thickness is almost constant at a deep position in the trench, but an overhang is observed at the upper position of the trench. For this reason, the presence of film formation species having a low sticking probability and the presence of film formation species having a high sticking probability are suggested. More specifically, it is considered that at least two types of film formation species contribute to film formation.
It is considered that the SiH.sub.4 gas reacts as expressed by equation (1) and influences film formation. EQU SiH.sub.4 .revreaction.SiH.sub.2 +H.sub.2 ( 1)
Since silylene (SiH.sub.2) generated by the reaction expressed by equation (1) is considered to have high reactivity and a sticking probability of about 1, it is assumed that the film formation species having a high sticking probability is SiH.sub.2. In this case, the sticking probability and density ratio of film formation species near the trench is regarded as a parameter for determining a film formation profile. For example, since the sticking probability of SiH.sub.2 is almost 1, such molecules having a high sticking probability form a film at the entrance portion of the trench. For this reason, the molecules cannot deeply enter the trench. Even a small amount of such reaction at an intermediate depth degrades the step coverage.
The method of performing the experiment with changing conditions as described above to determine a film formation thickness or a film formation profile has a lack of applicability, and optimum conditions which are satisfactory cannot be easily found. For this reason, a prediction method for correctly predicting the film formation thickness and film formation profile within a short period of time must be developed.
For papers which disclose the prediction method, Tatsuta et al: Simulation of CVD Step Coverage for SiH.sub.4 using Parallel Processing of DEMC Method, Computational Mechanics '95 (Processings of International Conference on Computational Engineering Science) Vol. 1, pp. 592 to 597, Springer-Verlag (1995), Toshiki Iino: Simulation for Semiconductor Film Formation Profile, Japan Society of Mechanical Engineers, 68th General Meeting Lecture Data, Vol. D (1994), pp. 447 to 449, or the like is known.
In the prediction method described in the above papers, a combination of an analysis of diluted gas flow and the simulation for film growing depending on the diluted gas flow is used. The Direct Simulation Monte Carlo (DSMC) method may be used for the analysis of diluted gas flow, and a string model, a cell model, or the like may be used for the simulation for film formation.
As a practical procedure for predicting film formation, a series of simulations in which the analysis of diluted gas flow in a computational domain, and a film is grown depending on the volume of sticking molecules are repeated until sticking of a required number of molecules is completed.
However, since such a conventional simulation method requires time integration for the analysis of diluted gas flow, when burying of a thin film into the trench described above is predicted, even if a computer having a relatively high speed is used, one month or one year or longer is required to perform one prediction treating film formation species having an especially low sticking probability. When a vector computation or a parallel process is employed, the required time can be shortened to some extent. However, when film formation species having a very low sticking probability is used, a long period of time is still required. For this reason, in the conventional method, the time required for prediction cannot be performed without considerably degrading prediction precision or considerably decreasing a prediction range.
More specifically, in the conventional simulation method of a problem that occurring in reality is probabilistic, a extremely long period of time is required to perform one prediction depending on the conditions. In addition, when the period of time is to be shortened, prediction precision is degraded, or an analysis range is limited to a specific range.